coaxialcylinder

A coaxial cylinder refers to one of two or more cylindrical surfaces or solids that share a common central axis. The simplest configuration is a pair of concentric cylinders, an inner cylinder of radius a and an outer cylindrical shell of radius b, often described as a cylindrical shell or annular cylinder when considering the region between radii. Coaxial cylinders are a basic geometric and engineering object used in mechanics, electromagnetism, fluid flow, heat transfer, and structural design.

Geometric and physical properties are frequently expressed per unit length for infinitely long or slender models. Volume of the annular region of length L is π(b^2 − a^2)L, and lateral surface areas are 2πaL and 2πbL. The mass moment of inertia of a hollow cylinder about its central axis is (1/2)M(a^2 + b^2) for mass M uniformly distributed between radii a and b. In electrostatics the capacitance per unit length between two coaxial conducting cylinders is C' = 2πε/ln(b/a), where ε is the permittivity of the intervening medium. Solutions of Laplace’s and Poisson’s equations in cylindrical coordinates commonly use coaxial configurations and exploit symmetry to reduce problems to ordinary differential equations.

Applications include coaxial cables (transmission lines with concentric conductors), pipe-within-pipe heat exchangers, bearings and journal assemblies, and laboratory apparatus for generating controlled radial fields. The coaxial form simplifies analysis and fabrication where rotational symmetry and uniform radial spacing are advantageous.